We study the joint effect of tidal torques and dynamical friction on the collapse of density peaks solving numerically the equations of motion of a shell of barionic matter falling into the central regions of a cluster of galaxies. We calculate the evolution of the expansion parameter, a(t), of the perturbation using a coefficient of dynamical friction ηcl obtained from a clustered system and taking into account the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-galaxies. We find that the tidal torques and the dynamical friction slow down the collapse of low-v (v < 3) peaks producing an observable variation of a(t) (Del Popolo & Gambera 1996,1997). As consequence we have a reduction of the mass bound to collapsed perturbations and a raising of the critical threshold, δc. Besides, we have a bias of dynamical nature arises because high-density peaks preferentially collapse to form halos within which visible objects. We calculate the selection function and using it and the prescriptions given by Bardeen et al. 1986 we find a value of the coefficient of bias, b = 2.25 on clusters scales for Rf = 4h–1Mpc comparable both with that obtained from the mean mass-to-light ratio of clusters, APM survey, or from N-body simulations combined with hydrodynamical models and with the values of b given by Kauffmann et al. 1996. This means that non-radial motions and dynamical friction play a significant role in determining the bias level.

Typical scales in the distribution of IRAS galaxies have been searched for with the unnormalized pair count method given by Mo et al.1. Samples consist of a) galaxies from QDOT with | b | ≥ 20°; b) galaxies from the IRAS faint source catalog(FSC) with f60 ≥ 0.3 Jy and | b | ≥ 30°. Galaxies with b ≥ 0 and b ≤ 0 were treated as independent samples in our analysis.

We expand on the work of Brainerd, Blandford & Smail (1996) (BBS), using a larger archival WFPC-2 dataset including many galaxy redshifts. It is clear from our data that the ellipticity distribution of images changes substantially with observed magnitude (figure 1, left) which is shown by simulations to be mainly the result of detection effects. We have detected a lensing signal, using a similar selection method to BBS and are also implementing a maximum likelihood method to constrain halo parameters. Using simulations, we show in figure 1 (right) that the signal is consistant with typical halo velocity dispersions of σ∗ ∼ 70–100 kms−1 However, the radial extent of the halos is less well constrained.

We compare the density fields from POTENT and IRAS. We vary the smoothing scale, and use a non-parametric test to obtain a value for the linear bias parameter b, as a function of offset c, which arises because the normalisation volumes for the two samples are different (Dekel et al., 1993). The smoothed fractional overdensities are related by δP = δI/b + c.

Because of the angular deficit around cosmic string, cold dark matter(CDM) gets the velocity toward the plane of moving string and wake is formed there. It means that CDM body is cut by string, two blocks move each other, and the overlapped region becomes wake. The wake and/or block size is determined by the horizon size at zi when the wake is triggered by the string. The nonlinearity and/or thickness of the wake depends on the moving length of CDM toward the wake which depends on zi, the line density and velocity of string.

Several scales' density fluctuations which exist in the early universe will first gravitationally collapse along one axis and make pancake-like structures. If the collapsed baryonic pancake heats up over 104K by shock formation, radiative cooling begins to work and mass accretion toward the central region will advance. Because of this effect, mass fraction of the high density layer becomes large. Densities and widths of the layers will reflect masses of structures (e.g. galaxy) which will be formed after caustics. In this respect, we assumed an Einstein-de Sitter universe dominated by cold dark matter (ΩDM = 0.9) and investigated the evolutions of fluctuations numerically using one-dimensional hydrodynamic plus N-body codes. We applied a new method for larger fluctuation scales; it is a hybrid method of Eulerian PPM and Zeldovich approximation and it can simulate around the central pancake region with high accuracy.

The MRC/1Jy sample of 559 radio sources with S408 MHz ≥ 0.95 Jy (McCarthy et al. 1996; Kapahi et al. in preparation) is a factor of 5 to 6 times deeper than the 3CRR sample; it is therefore, well suited for disentangling the redshift (z) and luminosity (P) dependence of several properties of extragalaxtic radio sources. Here we present results on the spectral index — redshift correlation for radio galaxies, based on a comparison of the well documented radio spectra (in the rest frame frequency range of about 1 to 16 GHz) of the following two matched-luminosity samples, (a) 14 high redshift radio galaxies (HRRG) from MRC with 2.0 < z < 3.2 and linear size i > 10 kpc, and (b) 21 intermediate z radio galaxies (IRRG) from 3CRR with 0.85 < z < 1.7 and l > 10 kpc. Both samples have P1.4 GHz in the range 1028 and 1028.8 WHz−1.

Using the particle-mesh method with 1283 grids and 643 particles, we have carried out a number of N-body simulations of the large scale structure for the cosmological model proposed by Fukuyama et al.(1996): this model contains the matter(Ω0) as well as a scalar field(Φ) with a finite mass that couples non-minimally with the scalar curvature R through the form of 1/2ηΦ2R, where η(= −80) is the coupling constant.

For simplicity, we have adopted the same values as those employed by Fukuyama et al.(1996) for all the parameters other than Ω0, fo which we have varied from 0.001 to 0.15. In performing our simulation, we further assume that only the density of matter ρ spatially fluctuates. The initial condition is created by perturbing the homogeneous distribution of the particles by means of the random Gaussian Harrison-Zeldovich spectrum.

The two-point correlation function ξ(r) is then compputed for each of the resulting structures to compare with the observational data(Davis and Peebles, 1983). It is interesting to note that the structure formation appears to be achieved rather straightforwardly with the scalar field model. However, in order to yield an agreement between the theoretical and the observational two-point correlation functions, we seem to require the Ω0 value much larger than 0.01 adopted by Fukuyama et al.(1996).

We compared the calculation performance of cosmological N-body simulations with and without GRAPE-4. A modified Barnes-Hut treecode was used for these simulations. GRAPE(GRAvity piPE) is a special-purpose computer for gravitational N-body simulations. The newest hardware GRAPE-4 achieved a quite high peak performance (1.08 Tflops). In cosmological N-body simulations, a large number of particles is required and fast algorithms such as Barnes-Hut treecode or P3M/PM are usually used. GRAPE-4 can accelearte such algorithms. In paticular, the PCI interface recently completed allows us to use fast host computer, thus it improved the performance of these fast algorithms. Figure 1 shows the CPU time per one timestep as functions of force calculation error for both systems with and without GRAPE-4.

We have observed a 0.7×1.2deg2 field in the SGP region with the UT / NAOJ Mosaic CCD Camera attached to the 40-inch Swope Telescope at Las Campanas Observatory, and constructed a sample of 1150 galaxies in the region down to R=20.5. Then we applied to the sample a new, objective cluster-finding technique, which is an improved variant of the so-called “matched-filter technique” pioneered by Postman et al. (1996). Using projected positions and apparent magnitudes of galaxies simultaneously, this technique can, not only find cluster candidates, but also estimate their redshifts and richnesses. A number of Monte Carlo simulations demonstrated enough accuracies of the estimations and much lower spurious detection rate than that by conventional cluster-finding methods which use only surface density of galaxies.

We compute the number counts of clusters of galaxies, the logN-logS relation, in several X-ray and submm bands on the basis of the Press—Schechter theory (Kitayama et al. 1998). We pay particular attention to a set of theoretical models which well reproduce the ROSAT 0.5–2 keV band logN-logS (Ebeling et al. 1997; Rosati et al. 1997), and explore possibilities to further constrain the models from future observations with ASCA and/or at submm bands. The latter is closely related to the European PLANCK mission and the Japanese LMSA project. We exhibit that one can break the degeneracy in an acceptable parameter region on the Ω0–σ8 plane by combining the ROSAT logN-logS and the submm number counts. Models which reproduce the ROSAT band logN-logS will have N(> S) ∼ (150–300)(S/10−12 erg cm−2 s−) −1.3 str−1 at S ≳ 10−12 erg cm−2 s−1 in the ASCA 2–10 keV band, and N(> Sv) ∼ (102–104)(Sv/100 mJy)−1.5 str−1 at Sv ≳ 100m J y in the submm (0.85mm) band. The amplitude of the logN-logS is very sensitive to the model parameters in the submm band. We also compute the redshift evolution of the cluster number counts and compare with that of the X-ray brightest Abell-type clusters (Ebeling et al. 1996). The results, although still preliminary, point to low density (Ω0 ∼ 0.3) universes. The contribution of clusters to the X-ray and submm background radiations is shown to be insignificant in any model compatible with the ROSAT logN-logS.

We present an investigation of the galaxy distribution in the huge underdense region between the Hercules, Coma and Local Superclusters, the so-called Northern Local Void (NLV), using void statistics (for details refer to Lindner et al. this Volume). Reshift data for galaxies and poor clusters of galaxies are available in low and high density regions as well. Samples of galaxies with different morphological type and various luminosity limits have been studied separately and void catalogues have been compiled from three different luminosity limited galaxy samples for the first time. Voids have been found using the empty sphere method which has the potential to detect and describe subtle structures in the galaxy distribution. Our approach is complementary to most other methods usually used in Large–Scale Structure studies.

We carried out a K′ band survey during August and September, 1994, in the south galactic pole region that covers 180.8 arcmin2 to K = 19 and 2.21 arcmin2 to K = 21 by the ANU 2.3 m telescope at SSO, Australia, equipped with PICNIC, developed at NAOJ. New galaxy number counts from K = 13 to 22 were obtained, which provided the best determination of the galaxy counts from K = 17.5 to 19.0 because of our large survey area. They were very consistent with Gardner, Cowie, & Wainscoat (1993, ApJL, 415, 9) and other observations to K < 19, however, they were larger than the galaxy counts of Saracco et al. (1997, AJ, 114, 887) with similar area and depth of survey around that magnitudes.

In this paper we investigate: a) The evolution of quasars on the basis of gravitational contraction model of proto-galaxies. This is done by studying the number density of quasars given by Veron catalogue [1] in different luminosity classes. The order of classes increase with increasing the luminosity of corresponding quasars. It is shown that the decay of quasars is more sensible to their luminosities as expected by assuming that they are evolved from the contraction of slowly rotating proto-galaxies. The role of the angular momentum in the evolution of galaxies is emphasized by the results obtained from the size-luminosity relation of about 40,000 normal galaxies given by LEDA database [2]. In the model mentioned above the normal galaxies are assumed to be evolved from the contraction of relatively fast rotating proto-galaxies. b) The filamentary structures and voids of the large scale universe by plotting the entire sky map of quasars in the galactic coordinate. This is done by assuming that these objects are at cosmological distances. The result which is plotted in the following figure, seems to show some spatial correlations of quasars distribution. The region of missing quasars is due to the dust clouds in our galaxy which block our view of other quasars. Note the voids and clumpy distribution of quasars looking like filaments.

During the period of galaxy formation, many small-length-scale perturbations superimposed on high-amplitude large-length-scale perturbations should have their overdensities boosted into the non-linear regime, while small-scale perturbations in other regions remain linear. The formation of the first galaxies in discrete, high overdensity regions may lead to an initial amplitude of the spatial correiatio? function of galaxies, ξ0, much higher than that expected from linear fluctuation theory. This initially high “bias” would consequently decrease to the near-unity values expected from local observations. Such a Decreasing Correlation Period (DCP) is detected in N-body simulations under certain conditions by several authors; Roukema (1993), Brainerd & Villumsen (1994), Roukema et al. (1997) and unpublished simulations by one of us (Yamashita).

The observed positions of quasars are fluctuated due to the gravitational lensing of the matters in our galaxy. The magnitude of fluctuation due to stars and MACHOs is of the order of a few micro-arc second (μas) ∼ 10 μas and its time scale is of the order of a few years ∼ hundreds years (Hosokawa et al. 1997). Such fluctuation will reflects the nature of the constituents, both visible and invisible, of our galaxy.

Galaxy distribution in clusters maybe affected by dynamical evolution of clusters and merging process of their member galaxies. In oreder to studey the effect, we study formation and evolution of galaxies in clusters by using N-body simulation. To identify galaxy size dark halos, we use the adaptive friends-of-friends algorithm (van Kampen 1995) at several red-shifts. At the same time, we treat galaxy merging and dark matter accretion to the galaxies by using the simple merging model. In this model we assume that galaxies have the merging cross section proportional to and if they encounter in small relative velocity (< Vmerge), they merge into one galaxy.

The topology of the Universe is a fundamental property of our Universe according to Friedmann-Lemaître models[3, 9, 7], but has not yet been reliably measured. As pointed out by Sato[12], the Universe may be finite even though flat or negatively curved: infinite volume of a hypersurface.

We propose a new method to estimate cosmological parameters using the baryon fraction of clusters of galaxies for a range of redshifts. The basic assumption is that the baryon fraction of clusters is constant, which is a reasonable assumption when it is averaged within a Mpc scale. We find that the baryon fraction vs. redshift diagram can estimate the cosmological parameters, since the derived value of the baryon fraction from observations depends on the adopted value of cosmological parameters through the angular diameter distance (e.g. Sasaki, S. 1996, PASJ48. L119).